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Efficient and robust approaches to the stability analysis and optimal control of large-scale multibody systems.

机译：大型多体系统的稳定性分析和最佳控制的有效而可靠的方法。

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摘要

Linearized stability analysis methodologies, system identification algorithms and optimal control approaches that are applicable to large scale, flexible multibody dynamic systems are presented in this thesis.; For stability analysis, two classes of closely related algorithms based on a partial Floquet approach and on an autoregressive approach, respectively, are presented in a common framework that underlines their similarity and their relationship to other methods. The robustness of the proposed approach is improved by using optimized signals that are derived from the proper orthogonal modes of the system. Finally, a signal synthesis procedure based on the identified frequencies and damping rates is shown to be an important tool for assessing the accuracy of the identified parameters; furthermore, it provides a means of resolving the frequency indeterminacy associated with the eigenvalues of the transition matrix for periodic systems. Unlike classical stability analysis methodologies, it does not require the linearization of the equations of motion of the system.; As an extension of the stability evaluation approaches, a robust system identification algorithm is developed to construct subspace plant models. The proposed system identification algorithm uniquely combines the methods of minimum realization and subspace identification. The proposed approach bypasses the computation of Markov parameters because the free impulse response of the system can be directly computed in the present computational environment. Minimum realization concepts were applied to identify the stability and output matrices. On the other hand, subspace identification algorithms construct a state space plant model of linear system by using computationally expensive oblique matrix projection operations. The proposed algorithm avoids this burden by computing the Kalman filter gain matrix and model dependency on external inputs in a small sized subspace. Balanced model truncation and similarity transformation form the theoretical foundation of proposed stability analysis approaches and system identification algorithms. The proposed stability analysis approaches and identification algorithms are all based on the assumption that the plant is a linear system. Numerically stable mathematical tools, singular value decomposition and least-square regression, are applied to improve the robustness of the system identification algorithms. Finally, a forward innovation model is constructed and estimates the input-output behavior of the system within a specified level of accuracy. The proposed stability and system identification algorithms are computationally inexpensive and consist of purely post processing steps that can be used with any multi-physics computational tool or with experimental data.; Optimal control methodologies that are applicable to comprehensive large-scale flexible multibody systems are presented. A classical linear quadratic Gaussian controller is designed: based on subspace plant identification, the linear quadratic regulator feedback gain and Kalman filter gain matrices are evaluated and online control is implemented. The linear quadratic Gaussian controller, a combination of the linear quadratic regulator and Kalman filter, is applied to control of large-scale flexible multibody systems. The online control uses a time adaptive scheme to compute the control inputs at a very low computational cost.
机译：本文提出了适用于大规模，柔性多体动力学系统的线性化稳定性分析方法，系统辨识算法和最优控制方法。为了进行稳定性分析，在共同的框架中介绍了分别基于部分Floquet方法和自回归方法的两类密切相关的算法，这些算法突显了它们的相似性以及它们与其他方法的关系。通过使用从系统的适当正交模式得出的优化信号，可以提高所提出方法的鲁棒性。最后，基于识别出的频率和阻尼率的信号合成程序被证明是评估识别出的参数准确性的重要工具。此外，它提供了一种解决与周期系统转换矩阵特征值相关的频率不确定性的方法。与经典的稳定性分析方法不同，它不需要线性化系统运动方程。作为稳定性评估方法的扩展，开发了鲁棒的系统识别算法来构建子空间工厂模型。提出的系统识别算法独特地结合了最小实现和子空间识别的方法。所提出的方法绕过了马尔可夫参数的计算，因为可以在当前计算环境中直接计算系统的自由冲激响应。最小实现概念被应用于识别稳定性和输出矩阵。另一方面，子空间识别算法通过使用计算量大的倾斜矩阵投影操作来构建线性系统的状态空间工厂模型。所提出的算法通过计算卡尔曼滤波器增益矩阵和模型对小尺寸子空间中外部输入的依赖性来避免这种负担。平衡的模型截断和相似度转换构成了所提出的稳定性分析方法和系统识别算法的理论基础。所提出的稳定性分析方法和识别算法均基于植物是线性系统的假设。使用数值稳定的数学工具，奇异值分解和最小二乘回归来提高系统识别算法的鲁棒性。最后，构建一个正向创新模型，并在指定的准确度水平内估算系统的输入输出行为。所提出的稳定性和系统识别算法在计算上不昂贵，并且由纯后处理步骤组成，可以与任何多物理场计算工具或实验数据一起使用。提出了适用于综合大规模柔性多体系统的最优控制方法。设计了经典的线性二次高斯控制器：基于子空间工厂识别，评估线性二次调节器反馈增益和卡尔曼滤波器增益矩阵，并实现在线控制。线性二次高斯控制器是线性二次调节器和卡尔曼滤波器的组合，用于控制大型柔性多体系统。在线控制使用时间自适应方案以非常低的计算成本来计算控制输入。

著录项

  • 作者

    Wang, Jielong.;

  • 作者单位

    Georgia Institute of Technology.;

  • 授予单位 Georgia Institute of Technology.;
  • 学科 Engineering Aerospace.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 218 p.
  • 总页数 218
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 航空、航天技术的研究与探索;
  • 关键词

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